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Accueil > Actualités > Séminaires > Séminaires 2009

Mardi 2 Juin 2009 à 11h00 - Amphi J

Sergey Golovin (Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russie)

Titre/Title :
Exact solutions to ideal magnetohydrodynamics equations

Contact :
Jan-Bert Flor

Résumé/Abstract :
Analytical modeling of plasma physics is based on the exact solutions
of the MHD equations. Due to the nonlinearity and complexity of the
equations, it is impossible to construct a general solution. However,
particular solutions of MHD equations that are based on Lie symmetry
analysis, allow for a describtion of the main features.
We present results of such a Lie symmetry analysis for the
construction and investigation of exact partially invariant solutions
to ideal MHD equations.
We discuss mainly two classes of solutions : partially invariant
solutions with respect to the group of rotations in 3D space, and
solutions with constant total pressure of stationary incompressible
MHD equations.

The first class of solutions describe a vortex motion with planar
trajectories and magnetic field lines driven by a spherical source.
Each magnetic line circumscribes the same planar curve in 3D space,
however, position and orientation of each curve is unique and is
prescribed by a certain directional field on a sphere.
We discuss singularities and characteristics of the flow governed by
the solution.

in the second part we observe stationary flows of an infinitely
conducting incompressible fluid. It is shown that contact magnetic
surfaces of such flows are translational surfaces, i.e. are swept out
by translating one curve rigidly along another curve. Explicit
examples of solutions possessing a significant functional
arbitrariness are discussed. Further we discuss possibilities for
application of Lie symmetry analysis to equations of rotating shallow
water equations, gas dynamics, and Navier-Stokes equations.